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At least 109 records · Page 6

Solvation Structure and Dynamics of Mg(TFSI) 2 Aqueous Electrolyte

Using ab initio molecular dynamics (AIMD) simulations, classical molecular dynamics (CMD) simulations, small-angle X-ray scattering (SAXS), and pulsed-field gradient nuclear magnetic resonance (PFG-NMR), the solvation structure and ion dynamics of magnesium bis(trifluoromethanesulfonyl)imide (Mg(TFSI) 2 ) aqueous electrolyte at 1, 2, and 3 m concentrations are investigated. From AIMD and CMD simulations, the first solvation shell of an Mg 2+ ion is found to be composed of six water molecules in an octahedral configuration and the solvation shell is rather rigid. The TFSI - ions prefer to stay in the second solvation shell and beyond. Meanwhile, the comparable diffusion coefficients of positive and negative ions in Mg(TFSI) 2 aqueous electrolytes have been observed, which is mainly due to the formation of the stable [Mg(H 2 O) 6 ] 2+ complex, and, as a result, the increased effective Mg ion size. Finally, the calculated correlated transference numbers are lower than the uncorrelated ones even at the low concentration of 2 and 3 m, suggesting the enhanced correlations between ions in the multivalent electrolytes. This work provides a molecular-level understanding of how the solvation structure and multivalency of the ion affect the dynamics and transport properties of the multivalent electrolyte, providing insight for rational designs of electrolytes for improved ion transport properties.

36 MATERIALS SCIENCE↗

Spin transition characteristics of molecular solvates of Cu{sup II} complexes with nitroxides: sensitivity to the packing type

A method for the synthesis of solvates of dinuclear heterospin complexes of bis(hexafluoroacetylacetonato)copper(II) with 2-(4-methylpyridin-3-yl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazole-3-oxide-1-oxyl (L{sup Me}) and 2-(4-ethylpyridin-3-yl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazole-3-oxide-1-oxyl (L{sup Et}) of the composition [Cu(hfac){sub 2}L{sup R}]{sub 2} · Solv (Solv = benzene, bromobenzene, toluene, o-xylene, p-xylene) was developed. It was found that a decrease in temperature induces structural transformations of the solid phases of the complexes followed by significant changes in the distances between the paramagnetic centers in the intramolecular exchange clusters {Cu"2"+-O"·-} from 2.321 to 1.974 Å. As a result, the temperature dependences of the effective magnetic moment μ{sub eff}(T) exhibit magnetic features similar to spin transitions. An analysis of the shape of the μ{sub eff}(T) curves suggested that the magnetic properties of the compounds under study depend primarily on the molecular packing. A comparison of the magneto-structural correlations typical of the [Cu(hfac){sub 2}L{sup R}]{sub 2} · Solv complexes studied in this work with the data obtained earlier for analogous solvates of heterospin polymer chain complexes showed that the spin transition characteristics of the [Cu(hfac){sub 2}L{sup R}]{sub 2} · Solv systems are much less sensitive to the change of the solvent than the corresponding characteristics of the heterospin polymers containing solvate molecules in the interchain space. The magnetic characteristics of the heterospin dimer molecules depend primarily on which cavity between the dimers is filled with solvate molecules. For solvates with monoclinic symmetry, changes in the solvent molecules occupying same-type cavities have almost no effect on the spin transition characteristics in the heterospin exchange cluster.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Revealing the Correlation between the Solvation Structures and the Transport Properties of Water-in-Salt Electrolytes

Water-in-salt (WIS) electrolytes containing 21 m lithium bis(trifluoromethane sulfonyl)imide (LiTFSI) have been considered as a safe and environment-friendly alternative to common organic electrolytes used in lithium-ion batteries. However, the relation between the solvation structures and transport properties of these materials remains elusive. Here, for this paper, we performed small-angle X-ray scattering (SAXS), small-angle neutron scattering (SANS), and X-ray pair distribution function (PDF) measurements of LiTFSI aqueous solutions at a wide range of concentrations. Combined with molecular dynamics simulations, the detailed solvation structures from long to short length scale were resolved. We found that the TFSI– solvation structures consist of TFSI– solvated structures and TFSI– networks; the former corresponds to solvent separated ion pairs, while the latter corresponds to contact ion pairs and cation–anion aggregates. In addition, we found that the relaxation time in the q range associated with the anion network structure exhibits the same concentration dependence as the viscosity. By combining the results from the experiments and simulations, this study revealed a correlation between the solvation structures of LiTFSI and the transport properties of the solutions, which is critical to understand the relation between the transport properties and the dynamics of the ions for imide-based lithium-ion salt aqueous electrolytes.

36 MATERIALS SCIENCE↗

Scaling Atomic Partial Charges of Carbonate Solvents for Lithium Ion Solvation and Diffusion

Lithium-ion solvation and diffusion properties in ethylene carbonate (EC) and propylene carbonate (PC) were studied by molecular simulation, experiments, and electronic structure calculations. Studies carried out in water provide a reference for interpretation. Classical molecular dynamics simulation results are compared to ab initio molecular dynamics to assess nonpolarizable force field parameters for solvation structure of the carbonate solvents. Quasi-chemical theory (QCT) was adapted to take advantage of fourfold occupancy of the near-neighbor solvation structure observed in simulations and used to calculate solvation free energies. The computed free energy for transfer of Li + to PC from water, based on electronic structure calculations with cluster-QCT, agrees with the experimental value. The simulation-based direct-QCT results with scaled partial charges agree with the electronic structure-based QCT values. The computed Li + /PF 6 - transference numbers of 0.35/0.65 (EC) and 0.31/0.69 (PC) agree well with NMR experimental values of 0.31/0.69 (EC) and 0.34/0.66 (PC) and similar values obtained here with impedance spectroscopy. These combined results demonstrate that solvent partial charges can be scaled in systems dominated by strong electrostatic interactions to achieve trends in ion solvation and transport properties that are comparable to ab initio and experimental results. Thus, the results support the use of scaled partial charges in simple, nonpolarizable force fields in future studies of these electrolyte solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Graph-Based Approaches for Predicting Solvation Energy in Multiple Solvents: Open Datasets and Machine Learning Models

The solvation properties of molecules, often estimated using quantum chemical simulations, are important in the synthesis of energy storage materials, drugs, and industrial chemicals. Here, we develop machine learning models of solvation energies to replace expensive quantum chemistry calculations with inexpensive-to-compute message-passing neural network models that require only the molecular graph as inputs. Our models are trained on a new database of solvation energies for 130,258 molecules taken from the QM9 dataset computed in five solvents (acetone, ethanol, acetonitrile, dimethyl sulfoxide, and water) via an implicit solvent model. Our best model achieves a mean absolute error of 0.5 kcal/mol for molecules with nine or fewer non-hydrogen atoms and 1 kcal/mol for molecules with between 10 and 14 non-hydrogen atoms. We make the entire dataset of 651,290 computed entries openly available and provide simple web and programmatic interfaces to enable others to run our solvation energy model on new molecules. This model calculates the solvation energies for molecules using only the SMILES string and also provides an estimate of whether each molecule is within the domain of applicability of our model. We envision that the dataset and models will provide the functionality needed for the rapid screening of large chemical spaces to discover improved molecules for many applications.

25 ENERGY STORAGE↗

Solvation and Dynamics of Sodium and Potassium in Ethylene Carbonate from ab Initio Molecular Dynamics Simulations

The development of sodium and potassium batteries offers a promising way to meet the scaling and cost challenges of energy storage. However, compared to Li + , several intrinsic properties of Na + and K + , including their solvation and dynamics in typical organic electrolytes utilized in battery applications, are less well-understood. Here in this paper, we report a systematic investigation of Na + and K + in ethylene carbonate (EC) using first-principles molecular dynamics simulations. Our simulations reveal significant differences in the solvation structure and dynamical properties of Na + and K + compared to Li + . We find that, in contrast to Li + which exhibits a well-defined first solvation shell, the larger Na+ and K+ ions show more disordered and flexible solvation structures. These differences in solvation were found to significantly influence the ion dynamics, leading to larger diffusion coefficients of Na + and K + compared to Li + . Our simulations also reveal a clear and interesting analog in the behavior of the ions in EC and aqueous environments, particularly in the specific ion effects on the solvent dynamics. Lastly, this work provides fundamental understanding of the intrinsic properties of Na + and K + in organic electrolytes, which may ultimately influence the intercalation mechanism at the electrode–electrolyte interface and therefore battery performance, lifetime, and safety.

25 ENERGY STORAGE↗

Role of Solvent Rearrangement on Mg2+ Solvation Structures in Dimethoxyethane Solutions Using Multimodal NMR Analysis

One of the main impediments faced for predicting important emergent properties of a multivalent electrolyte (such as conductivity and electrochemical stability) is the lack of quantitative analysis of ion-ion and ion-solvent interactions, which manifest in solvation structures and dynamics. In particular, the role of ion-solvent interactions is still unclear in cases where the strong electric field from multivalent cations can influence structural evolution of lower permittivity organic solvent molecules on solvation structure. These influences are commonly refered to as electrostriction pheonmena. Using quantitative 1H, 19F, 17O, and 25Mg NMR together with 19F nuclear spin relaxation and diffusion measurments, we find an unusual correlation between ion concentration and solvation structure of Mg(TFSI)2 salt in dimethoxyethane (DME) solution. The domiant solvation structure evolves from contact ion pairs (i.e. [Mg(TFSI)(DME)1-2]+) to fully solvated clusters (i.e. [Mg(DME)3]2+) as salt concentration increases or as temperature decreases. This transition is coupled to a phase separation, which we study here between 0.06 M and 0.36 M. Subsequent analysis is based on an explanation of the electrostriction phenomena and the competion between solvent molecules and TFSI anions for cation coordination.

Chen, Ying↗

Prediction and Experimental Verification of Electrolyte Solvation Structure from an OMol25-Trained Interatomic Potential

A molecular-level understanding of electrolyte solvation structure and ion–ion correlations is critical to developing next-generation battery chemistries. Atomistic simulation capabilities with sufficient accuracy, speed, and transferability to deliver reliable structural insights while avoiding arduous system-specific reparameterization are thus highly desirable. Machine learning interatomic potentials (MLIPs) trained on large, chemically diverse data sets are revolutionizing computational chemistry, enabling molecular dynamics simulations of battery electrolytes with near-DFT accuracy over 10,000× faster than DFT. While previous MLIP training data sets with suitable elemental coverage for electrolytes have been based on inorganic materials, the Open Molecules 2025 (OMol25) data set provides large-scale molecular DFT MLIP training data with broad elemental coverage and specifically samples tens of millions of electrolyte configurations. Here, we integrate computational modeling with experimental validation to systematically assess the ability of large-scale MLIPs pretrained on materials data or on OMol25 to accurately resolve nanoscale structural organization and ion-solvation characteristics in Na-ion battery electrolytes across diverse physicochemical conditions and compositional regimes. We find that the OMol25-trained Universal Model of Atoms (UMA-OMol) predicts experimentally measured densities and X-ray structure factors in substantially better agreement compared to state-of-the-art models trained only on inorganic materials data. Using UMA-OMol, we further analyze systematic trends in solvation structure as a function of cation identity, anion chemistry, salt concentration, and solvent topology. We observe that increasing system temperature amplifies the heterogeneity within the solvation environment, perturbing cation–solvent interactions and promoting the formation of contact ion pairs (CIPs). Moreover, subtle variations in the solvent topology of glyme-based electrolytes cause pronounced changes in ion correlations and solvation structure. The experimental agreement and microscopic insights shown here position OMol25-trained MLIPs as a practical route to predictive, high-throughput electrolyte simulations beyond the limits of classical force fields and direct DFT molecular dynamics, serving as a powerful tool for accelerating the design of next-generation Na-ion battery electrolytes and beyond.

MLIPs↗

Solvation Structure of Methanol-in-Salt Electrolyte Revealed by Small-Angle X-ray Scattering and Simulations

The solvation structure of water-in-salt electrolytes was thoroughly studied, and two competing structures—anion solvated structure and anion network—were well-defined in recent publications. To further reveal the solvation structure in those highly concentrated electrolytes, particularly the influence of solvent, methanol was chosen as the solvent for this proposed study. In this work, small-angle X-ray scattering, small-angle neutron scattering, Fourier-transform infrared spectroscopy, and Raman spectroscopy were utilized to obtain the global and local structural information. With the concentration increment, the anion network formed by TFSI - became the dominant structure. Meanwhile, the hydrogen bonds among methanol were interrupted by the TFSI - anion and formed a new connection with them. Further, molecular dynamic simulations with two different force fields (GAFF and OPLS-AA) are tested, and GAFF agreed with synchrotron small-angle X-ray scattering/wide-angle X-ray scattering (SAXS/WAXS) results well and provided insightful information about molecular/ion scale solvation structure. This article not only deepens the understanding of the solvation structure in highly concentrated solutions, but more importantly, it provides additional strong evidence for utilizing SAXS/WAXS to validate molecular dynamics simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Mass action model of solution activity via speciation by solvation and ion pairing equilibria

Abstract Solutes and their concentrations influence many natural and anthropogenic solution processes. Electrolyte and solution models are used to quantify and predict such behavior. Here we present a mechanistic solution model based on mass action equilibria. Solvation and ion pairing are used to model speciated solute and solvent concentrations such that they correlate to a solution’s vapor pressure (solvent activity) according to Raoult’s law from dilute conditions to saturation. This model introduces a hydration equilibrium constant ( K ha ) that is used with either an ion dissociation constant ( K id ) or a hydration modifier ( m ) with an experimentally determined ion dissociation constant, as adjustable parameters to fit vapor–liquid equilibrium data. The modeled solvation equilibria are accompanied by molecular dynamics (MD) studies that support a decline in the observed degree of solvation with increased concentration. MD calculations indicate this finding is a combination of a solvent that solvates multiple solutes, and changes in a solute’s solvation sphere, with the dominant factor changing with concentration. This speciation-based solution model is lateral to established electrostatics-based electrolyte theories. With its basis in mass action, the model can directly relate experimental data to the modeled solute and solvent speciated concentrations and structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Role of solvation site segmental dynamics on ion transport in ethylene-oxide based side-chain polymer electrolytes

Ion conducting capability is often imparted to polymeric materials through short polyether side-chains, and yet the impact of this graft polymer architecture on ion solvation and conduction has not been fully explored. Here, we use a combination of impedance spectroscopy, vibrational spectroscopy, and atomistic molecular dynamics (MD) to compare the conductivity, ionic interactions, and polymer dynamics in a series of graft polyether electrolytes. We find that in poly[(oligo ethylene oxide)methyl ether methacrylate] (POEM), a widely used graft polymer electrolyte, the ionic conductivity drops more than an order of magnitude as the side-chain length is decreased from nine ethylene oxide (EO) units to three. This difference in conductivity is unexplained by differences in the calorimetric glass transition temperature (T g ), which varies only slightly with side-chain length. Furthermore, through vibrational spectroscopy and MD simulations we demonstrate that both linear and graft polyethers solvate Li⁺ ions effectively and dissociate them from large counterions, irrespective of side-chain length. Li⁺ ions do, however, show preferential solvation by EO units far from the methacrylate backbone. Similarly, EO units far from the backbone show enhanced segmental dynamics, while those near the immobile methacrylate group move substantially more slowly, as quantified by bond vector autocorrelation relaxation times. This heterogeneity in both ion solvation and local segmental relaxation explains variation in ion conductivity where material-averaged properties such as T g and number of free ions fail to do so. Importantly, the ionic conductivity is dictated primarily by the segmental mobility of the EO units which form effective solvation sites, rather than system-wide dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Systematic improvement of redox potential calculation of Fe(III)/Fe(II) complexes using a three-layer micro-solvation model

Electrochemical transformations of metal ions in aqueous media are challenging to model accurately due to the dynamic solvation structure surrounding ions at different charge states. Predictive modeling at the atomistic scale is essential for understanding these solvation architectures but is often computationally prohibitive. In this contribution, we present a simple, fast, and accurate three-layer micro-solvation model to evaluate the redox potential of metal ions in aqueous solutions. Our model, developed and validated for Fe 3+ /Fe 2+ redox potentials, combines the DFT-based geometry optimizations of the octahedral Fe complex with two layers of explicit water molecules to capture solute–solvent interactions and an implicit solvation model to account for bulk solvent effects. This approach yields accurate predictions for Fe 3+ /Fe 2+ redox potentials in water, achieving errors of 0.02 V with ωB97X-V, 0.01 V with ωB97X-D3, 0.04 V with ωB97M-V, and 0.02 V with B3LYP-D3 functionals. We further demonstrate the generality of our model by applying it to additional metal complexes, including the challenging Fe(CN) 6 3−/4− system, where our model successfully achieves close agreement with experimental values, with an error of 0.07 V and an average error of 0.21 V for all five systems. In summary, the presented simple solvation model has broad applicability and potential for enhancing computational efficiency in redox potential predictions across various chemical and industrial processes of metal ions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Electrostatic solvation free energies of charged hard spheres using molecular dynamics with density functional theory interactions

Determining the solvation free energies of single ions in water is one of the most fundamental problems in physical chemistry and yet many unresolved questions remain. In particular, the ability to decompose the solvation free energy into simple and intuitive contributions will have important implications for models of electrolyte solution. In this paper, we provide definitions of the various types of single ion solvation free energies based on different simulation protocols. We calculate solvation free energies of charged hard spheres using density functional theory interaction potentials with molecular dynamics simulation and isolate the effects of charge and cavitation, comparing to the Born (linear response) model. We show that using uncorrected Ewald summation leads to unphysical values for the single ion solvation free energy and that charging free energies for cations are approximately linear as a function of charge but that there is a small non-linearity for small anions. The charge hydration asymmetry for hard spheres, determined with quantum mechanics, is much larger than for the analogous real ions. Finally, this suggests that real ions, particularly anions, are significantly more complex than simple charged hard spheres, a commonly employed representation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Improving accuracy of electrochemical capacitance and solvation energetics in first-principles calculations

Here, reliable first-principles calculations of electrochemical processes require accurate prediction of the interfacial capacitance, a challenge for current computationally efficient continuum solvation methodologies. We develop a model for the double layer of a metallic electrode that reproduces the features of the experimental capacitance of Ag(100) in a non-adsorbing, aqueous electrolyte, including a broad hump in the capacitance near the potential of zero charge and a dip in the capacitance under conditions of low ionic strength. Using this model, we identify the necessary characteristics of a solvation model suitable for first-principles electrochemistry of metal surfaces in non-adsorbing, aqueous electrolytes: dielectric and ionic nonlinearity, and a dielectric-only region at the interface. The dielectric nonlinearity, caused by the saturation of dipole rotational response in water, creates the capacitance hump, while ionic nonlinearity, caused by the compactness of the diffuse layer, generates the capacitance dip seen at low ionic strength. We show that none of the previously developed solvation models simultaneously meet all these criteria. We design the nonlinear electrochemical soft-sphere solvation model which both captures the capacitance features observed experimentally and serves as a general-purpose continuum solvation model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Solvation of furfural at metal–water interfaces: Implications for aqueous phase hydrogenation reactions

Metal–water interfaces are central to understanding aqueous-phase heterogeneous catalytic processes. However, the explicit modeling of the interface is still challenging as it necessitates extensive sampling of the interfaces’ degrees of freedom. Herein, we use ab initio molecular dynamics (AIMD) simulations to study the adsorption of furfural, a platform biomass chemical on several catalytically relevant metal–water interfaces (Pt, Rh, Pd, Cu, and Au) at low coverages. We find that furfural adsorption is destabilized on all the metal–water interfaces compared to the metal–gas interfaces considered in this work. This destabilization is a result of the energetic penalty associated with the displacement of water molecules near the surface upon adsorption of furfural, further evidenced by a linear correlation between solvation energy and the change in surface water coverage. To predict solvation energies without the need for computationally expensive AIMD simulations, we demonstrate OH binding energy as a good descriptor to estimate the solvation energies of furfural. Using microkinetic modeling, we further explain the origin of the activity for furfural hydrogenation on intrinsically strong-binding metals under aqueous conditions, i.e., the endothermic solvation energies for furfural adsorption prevent surface poisoning. In conclusion, our work sheds light on the development of active aqueous-phase catalytic systems via rationally tuning the solvation energies of reaction intermediates.

aqueous-phase hydrogenation↗

Solvation governs cation transference in glyme-based lithium battery electrolytes

The efficacy of electrochemical systems is governed by the cation transference number, which represents the fraction of current carried by the working ion. Energy is wasted when field-induced motion also drives anions and solvent molecules, decreasing the transference number to near-zero. We present a systematic study of cation transference in a series of electrolytes: tetraglyme (TG), octaglyme (OG), and poly(ethylene oxide) (PEO) mixed with lithium bis(trifluoromethanesulfonyl)imide. In all three electrolytes, starting from the dilute salt concentration limit, the experimentally measured cation transference number decreases with increasing concentration, reaching a minimum between -0.1 and -0.2, before rising back to positive values. Explicit measurements of field-induced species' velocities by electrophoretic nuclear magnetic resonance indicate that negative cation transference numbers in TG and OG electrolytes are dictated by solvation interactions with minimal contribution from anion-cation interactions. Simulation-based solvation structures indicate that OG serves as a bridge between TG and PEO. Multi-charge positive clusters, which are negligible in TG, become increasingly important at higher chain lengths (OG and PEO). As migrating cations drag their solvation shells, this solvation-induced motion is amplified in glyme electrolytes because of covalent interactions between solvating glyme molecules and free glyme molecules.

Im, Julia↗

Understanding Lithium Solvation and Diffusion through Topological Analysis of First-Principles Molecular Dynamics

The performance of lithium-ion batteries is strongly influenced by the ionic conductivity of the electrolyte, which depends on the speed at which Li ions migrate across the cell and relates to their solvation structure. The choice of solvent can greatly impact, both, the solvation and diffusivity of Li ions. In this work, we present our application of the topological techniques to extract and predict such behavior in the data generated by the first-principles molecular dynamics simulation of Li ions in an important organic solvent -ethylene carbonate. More specifically, we use the scalar topology of the electron charge density field to analyze the evolution of the solvation structures. This allows us to derive a parameter-free bond definition for lithium-oxygen bonds, to provide a quantitative measure for bond strength, and to understand the regions of influence of each atom in the simulation. This has provided new insights into how and under what conditions certain bonds may form and break. As a result, we can identify and, more importantly, predict, unstable configurations in solvation structures. This can be very useful in understanding when small changes to the atoms' movements can cause significantly different bond structures to evolve. Ultimately, this promises to allow scientists to explore lithium ion solvation and diffusion more systematically, with the aim of new insights and potentially accelerating the calculations themselves.

36 MATERIALS SCIENCE↗

Coordination Chemistry of Solvated Metal Ions in Soft Donor Solvents

The structures of hexaammine solvated indium(III) and thallium(III) ions in liquid ammonia solution are determined by EXAFS. Both complexes have regular octahedral coordination geometry with mean In-N and Tl-N bond distances of 2.23(1) and 2.29(2) Å, respectively. Ammine solvated thallium(III) in liquid ammonia is characterized with 205Tl NMR measurements. Solvents such as liquid ammonia, N,N-dimethylthioformamide (DMTF), trialkyl and triphenyl phosphite and phosphine are strong electron pair donors and thereby able to form bonds with a large covalent contribution with strong electron pair acceptors. A survey of reported structures of ammine, DMTF, trialkyl and triphenyl phosphite and phosphine solvated metal ions in the solid state and solution is presented. The M-N and M-S bond distances in ammine and DMTF solvated metal ions are compared with the M-O bond distance in the corresponding metal ion hydrates, expected to form mainly electrostatic interactions with metal ions. The d10 metal ions have high ability to form bonds with a high degree of covalency with increasing ability down the group and with decreasing charge of the metal ion. The difference in M-N and M-O bond distances between ammine solvated and hydrated metal ions with the same coordination geometry decreases significantly with the increasing ability of the metal ion to form bonds with a large covalent contribution. This difference correlates well with the covalent bonding index, γM2*r.

Biochemistry & Molecular Biology↗